Related papers: On Generalized Free Electron Laser Equation
Let $(\mu_{\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\alpha})$ be a net in $]0,+\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\lambda)$ exists for all…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
Several methods have been proposed in the literature to improve Free Electron Laser output by transforming the electron phase-space before entering the FEL interaction region. By utilising `beam by design' with novel undulators and other…
We develop a new generalized form of the fractional kinetic equation involving a generalized k-Bessel function. The generalized $k$-Mittag-leffler function $E^{\gamma,q}_{k,\alpha,\beta}(.)$ is discussed in terms of the solution of the…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
Here a detailed formalism to achieve an analytical solution of a lossy high power Yb-doped silica fiber laser is introduced. The solutions for the lossless fiber laser is initially attained in detail. Next, the solution for the lossy fiber…
In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for…
A relativistic quantum mechanical model to describe the quantum FEL dynamics has been developed. Neglecting the spin of electrons in the impacting beam, this model is based on the Klein-Gordon equation coupled to the Poisson equation for…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
The massive electrodynamics is applied to the Dirac equation to find the generalized Volkov solution with massive photon field. The resulting equation is the Riccati equation which cannot be solved in general. We use the approximative…
We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in…
The interaction between noncolinear laser and relativistic electron beams in static magnetic undulator has been studied within the framework of dispersion equations. For a free-electron laser without inversion (FELWI), the threshold…
It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…
In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and…
We propose and discuss a numerical method to model electromagnetic emission from the oscillating relativistic charged particles and its coherent amplification. The developed technique is well suited for free electron laser simulations, but…
If the quantum mechanical recoil of the electron due to its scattering from the undulator and laser fields dominates the dynamics, a regime of the free-electron laser emerges where quantum effects lead to a drastic change in the radiation…
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a…
High-gain Free Electron Laser (FEL) is one of the many electron-beam instabilities that have a number of common features linking the shot noise, the amplification and the saturation. In this paper, we present a new, model-independent…
Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using…
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…